Fabri, Honoré
,
Tractatus physicus de motu locali
,
1646
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<
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ſunt vt radices AEAT, id eſt tempus quo percurritur AE eſt ad tem
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pus, quo percurritur AT, vt AE ad mediam proportionalem inter AE
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AT, vel vt AD ad mediam proportionalem inter AD AR; quippe AD
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eſt ad AR vt AE ad AT. </
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<
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id
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">Galileus verò demonſtrat rationem iſtorum temporum eſſe compoſi
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tam ex ratione longitudinem planorum & ex ratione ſubduplicata al
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titudinum eorumdem permutatim accepta: pro quo obſerua à Galileo
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rationem duplicatam appellari duplam, & ſubduplicatam appellari ſub
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duplam. </
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<
s
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">Obſeruabis denique plurima ex his colligi poſſe præſertim ex Th. 27.
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quæ quia ſunt purè geometrica, certè phyſicę minimè competunt; aliqua
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tamen omittere non poſſum. </
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">Primò, ſi ſint duo plana inæqualia ad angulum rectum, qui ſuſtinea
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tur ab horizontali, determinari poſſunt tempora deſcenſuum ſit enim
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triangulum orthogonium ABE, ita vt AE ſit horizontalis; </
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G indefinita perpendicularis in baſim AE; </
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">tùm FA perpendicularis in
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AB; </
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">tùm FC perpendicularis in BE; </
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<
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">tùm denique GE in BE; </
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<
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">dico BA
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BFBC percurri temporibus æqualibus, item BE, BG, EG, etiam æqua
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libus; </
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">igitur tempus, quo percurritur BA eſt ad tempus quo percurri
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tur BE, vt tempus, quo percurritur BF ad tempus quo percurritur BG;
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hæc porrò ſunt in ſubduplicata ratione BFBG vel BC, & BE. </
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<
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">Secundò, ſi planum ſuſtinens angulum rectum non ſit parallelum
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horizonti 6. res ſimiliter determinari poterit; </
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">ſit enim triangulum or
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thogonium ABC ex B, ducatur perpendicularis deorſum indefinitè BF,
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tùm EA in AB, tùm DC in CB, tùm EH parallela DC, tùm GC in A
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C; </
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<
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">denique AG parallela BF; dico quod BABEHE AE percurren
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tur æqualibus temporibus item BCCDBD. </
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<
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">Tertiò, ſiue deſcendat ex B in C per lineam perpendicularem BC,
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ſiue ex A per inclinatam AC, eodem modo deſcendet ſiue per CD, ſiue
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per CE; ratio eſt clara, quia acquirit æqualem velocitatem ſiue ex A ſi
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ue ex B deſcendat pet Th. 20. erit autem tempus per CE ad tempus per
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CD, vt CE ad CD per Th.23.& motus per CE ad motum per CD, vt
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CD ad CE per Th.6. poſito initio motus in C. </
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<
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">Quartò, præuio motu ex A vel ex B ad C poteſt inueniri inclinata,
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per quam mobile pergat moueri motu ſcilicet naturaliter accelerato, ita
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vt æquali tempore illam conficiat; </
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<
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">ſi enim BC conficiet dato tempore; </
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igitur CF triplum CB conficiet tempore æquali; </
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<
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">ſit autem planum ho
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rizontale EDK ad quod ex C ducendum ſit planum inclinatum, quod
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eodem tempore percurratur, quo CF, diuidatur CF bifariam in H, & ex
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puncto H fiat arcus CK, ducaturque CK: </
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">Dico CF & CK æquali tem
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pore confici per Th. 27. modò ex quiete C procedat motus: </
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">ſimiliter aſ
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ſumi poteſt alia horizontalis LM ducto arcu LF ex centro H; </
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<
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id
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">nam CL
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& CF æquali tempore percurruntur; </
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<
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id
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">ſi verò præſupponatur motus præ
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uius ex A vel ex B, haud dubiè CK breuiori tempore percurretur, quàm
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CF, idem dico de CL; </
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<
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">alioqui CE & CI eodem præuio motu ſuppo </
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